The goal of the learner is to minimize regret, \(\operatorname{Reg}_T\) , to the optimal policy \(\pi _{\ell ^\star }\) . The primary difference between our setting and that of [1]}, [2]}, other than the fact that we are considering a particular function class \(\mathcal {G}_\mathcal {F}^\mathcal {A}\) , is that our losses are noiseless, while the prior works allow for some noise that is mean zero conditional on the history. We have the following regret bound:
